The programmable gain amplifier is an indispensable component in digital communications systems. A programmable gain amplifier is provided for boosting the gain of signals such that received input signals from radio frequency front-end circuits can be adjusted to a suitable level. Accordingly, by doing so, the demand for dynamic range of a base band analog-digital converter (ADC) is reduced. Moreover, if the input signal has a DC offset, a gain amplifier can be utilized for boosting the DC offset of the input current. After being processed by the gain amplifier, the resulting signals will saturate the following baseband ADC stage. As a result of coupling of the RF input to local oscillators, due to input of mixers in the applied architectures for low intermediate frequency (low IF) and zero intermediate frequency (zero IF), it is highly likely that interference resulting from signals being mixed will be introduced, resulting in unavoidable DC offset. Therefore, it is desired to incorporate a DC offset cancellation circuit in the design for resolving the aforementioned problem. Furthermore, due to mismatch of components or manufacturing process flaws, the DC offset can also be observed in integrated circuits used in gain amplifier circuits. The architecture proposed in the present invention offers a solution for resolving such DC offset problem and a method for allowing the system to rapidly converge to stable status.